Simplify the following expression and state the condition under which the simplification is valid. You can assume that $p \neq 0$. $x = \dfrac{2p}{2(4p - 3)} \div \dfrac{3p}{5(4p - 3)} $
Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{2p}{2(4p - 3)} \times \dfrac{5(4p - 3)}{3p} $ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 2p \times 5(4p - 3) } { 2(4p - 3) \times 3p } $ $ x = \dfrac{10p(4p - 3)}{6p(4p - 3)} $ We can cancel the $4p - 3$ so long as $4p - 3 \neq 0$ Therefore $p \neq \dfrac{3}{4}$ $x = \dfrac{10p \cancel{(4p - 3})}{6p \cancel{(4p - 3)}} = \dfrac{10p}{6p} = \dfrac{5}{3} $